Question

A parallel combination of pure inductor and capacitor is connected across a source of alternating e.m.f. \( e \). The currents flowing through an inductor and capacitor are \( i_L \) and \( i_C \) respectively. In this parallel resonant circuit, the condition for currents \( i, i_L, i_C \) (i.e. \( i \) = net r.m.s. current in the circuit) is

• A. \( i = 0, i_L = i_C \neq 0 \)
• B. \( i \neq 0, i_L = i_C = 0 \)
• C. \( i \neq 0, i_L = i_C \)
• D. \( i = 0, i_L \neq i_C \)

Hint:

In parallel resonant circuits, at resonance, the net current is zero, and the currents in the inductor and capacitor are equal in magnitude but opposite in direction.

Answer 1

The Correct Option is A

Step 1: Understanding the resonance condition.
In a parallel resonant circuit, the current in the main circuit \( i \) is zero at resonance, because the currents through the inductor \( i_L \) and capacitor \( i_C \) are equal and opposite. Therefore, \( i_L = i_C \), and the net current \( i \) is zero.

Step 2: Analyzing the options.
- (A) \( i = 0, i_L = i_C \neq 0 \) is correct because at resonance, the inductor and capacitor currents cancel each other out, but are equal in magnitude. - (B) \( i \neq 0, i_L = i_C = 0 \) is incorrect because at resonance, there is no net current, and both inductor and capacitor have non-zero currents. - (C) \( i \neq 0, i_L = i_C \) is incorrect because \( i = 0 \) at resonance. - (D) \( i = 0, i_L \neq i_C \) is incorrect because at resonance, \( i_L = i_C \).

Step 3: Conclusion.
The correct answer is (A), as it correctly describes the condition for resonance in a parallel LC circuit.